TY - JOUR
T1 - On Polynomial Maximum Entropy Method for Classical Moment Problem
AU - Ding , Jiu
AU - Rhee , Noah H.
AU - Zhang , Chenhua
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 117
EP - 127
PY - 2018
DA - 2018/05
SN - 8
DO - http://doi.org/10.4208/aamm.2014.m504
UR - https://global-sci.org/intro/article_detail/aamm/12080.html
KW - 
AB - <p style="text-align: justify;">The maximum entropy method for the Hausdorff moment problem suffers
from ill conditioning as it uses monomial basis {1,$x$,$x^2$,···,$x^n$}. The maximum entropy
method for the Chebyshev moment probelm was studied to overcome this drawback
in [4]. In this paper we review and modify the maximum entropy method for the
Hausdorff and Chebyshev moment problems studied in [4] and present the maximum
entropy method for the Legendre moment problem. We also give the algorithms of
converting the Hausdorff moments into the Chebyshev and Lengendre moments, respectively,
and utilizing the corresponding maximum entropy method.</p>